Solve 5/3-2/8x+5/6x-1/3=frac{9}{8}x-frac{168}{3}

$$\frac { 5 } { 3 } - \frac { 2 } { 8 } x + \frac { 5 } { 6 } x - \frac { 1 } { 3 } = \frac { 9 } { 8 } x - \frac { 168 } { 3 }$$

Solve for x

$$x = \frac{1376}{13} = 105\frac{11}{13} \approx 105.846153846$$

Steps for Solving Linear Equation

Reduce the fraction \frac{2}{8} to lowest terms by extracting and canceling out 2.

$$\frac{5}{3}-\frac{1}{4}x+\frac{5}{6}x-\frac{1}{3}=\frac{9}{8}x-\frac{168}{3}$$

Combine -\frac{1}{4}x and \frac{5}{6}x to get \frac{7}{12}x.

$$\frac{5}{3}+\frac{7}{12}x-\frac{1}{3}=\frac{9}{8}x-\frac{168}{3}$$

Since \frac{5}{3} and \frac{1}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5-1}{3}+\frac{7}{12}x=\frac{9}{8}x-\frac{168}{3}$$

Subtract 1 from 5 to get 4.

$$\frac{4}{3}+\frac{7}{12}x=\frac{9}{8}x-\frac{168}{3}$$

Divide 168 by 3 to get 56.

$$\frac{4}{3}+\frac{7}{12}x=\frac{9}{8}x-56$$

Subtract \frac{9}{8}x from both sides.

$$\frac{4}{3}+\frac{7}{12}x-\frac{9}{8}x=-56$$

Combine \frac{7}{12}x and -\frac{9}{8}x to get -\frac{13}{24}x.

$$\frac{4}{3}-\frac{13}{24}x=-56$$

Subtract \frac{4}{3} from both sides.

$$-\frac{13}{24}x=-56-\frac{4}{3}$$

Convert -56 to fraction -\frac{168}{3}.

$$-\frac{13}{24}x=-\frac{168}{3}-\frac{4}{3}$$

Since -\frac{168}{3} and \frac{4}{3} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{13}{24}x=\frac{-168-4}{3}$$

Subtract 4 from -168 to get -172.

$$-\frac{13}{24}x=-\frac{172}{3}$$

Multiply both sides by -\frac{24}{13}, the reciprocal of -\frac{13}{24}.

$$x=-\frac{172}{3}\left(-\frac{24}{13}\right)$$

Multiply -\frac{172}{3} times -\frac{24}{13} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-172\left(-24\right)}{3\times 13}$$

Do the multiplications in the fraction \frac{-172\left(-24\right)}{3\times 13}.

$$x=\frac{4128}{39}$$

Reduce the fraction \frac{4128}{39} to lowest terms by extracting and canceling out 3.

$$x=\frac{1376}{13}$$